Abstract
Using dashed strings is an approach recently introduced in Constraint Programming (CP) to represent the domain of string variables, when solving combinatorial problems with string constraints. One of the most important string constraints is that of regular membership: \(\textsc {regular} (x, R)\) imposes string x to be a member of the regular language defined by automaton R. The regular constraint is useful for specifying complex constraints on fixed length finite sequences, and regularly appears in CP models. Dealing with regular is also desirable in software testing and verification, because regular expressions are often used in modern programming languages for pattern matching. In this paper, we define a regular propagator for dashed string solvers. We show that this propagator, implemented in the G-Strings solver, is substantially better than the current state-of-the-art. We also demonstrate that many regular constraints appearing in string solving benchmarks can actually be tackled by dashed strings solvers without explicitly using regular.
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Notes
- 1.
Note that \(maxl(R) \ne \max \{ |w| ~|~ w \in L(R), |w| \le \lambda \}\), which is less easy to compute. If \(maxl(R) > \lambda \), we set \(maxl(R) = \lambda \): this is a correct but not optimal upper bound.
- 2.
Note this is different from the iterated concatenation of strings. For example, encoding
with 
is unsound because this actually encodes the constraint 
(e.g., 
). - 3.
We used Z3str3 4.6.2 and CVC4 1.5. The source code of the experiments is publicly available at: https://bitbucket.org/robama/exp_cp_2018.
- 4.
Precisely, this is the instance 489 of the HammingDistance class. G-Decomp with \(\lambda = 500\) takes 454.6 s to detect the unsatisfiability. Clearly, we can only prove that there is no solution where all string variables x have length \(|x| \le \lambda \).
with 
is unsound because this actually encodes the constraint 
(e.g., 
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Acknowledgments
This work is supported by the Australian Research Council (ARC) through Linkage Project Grant LP140100437 and Discovery Early Career Researcher Award DE160100568.
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Amadini, R., Gange, G., Stuckey, P.J. (2018). Propagating Regular Membership with Dashed Strings. In: Hooker, J. (eds) Principles and Practice of Constraint Programming. CP 2018. Lecture Notes in Computer Science(), vol 11008. Springer, Cham. https://doi.org/10.1007/978-3-319-98334-9_2
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